Inkjet printing papers are suitable to form high-quality images with an inkjet printer. However, inkjet printing papers are normally expensive and are therefore not suitable for high-volume printing.
On the other hand, high-quality coated papers for commercial printing (hereafter called commercial printing paper(s)) are of high quality as well as comparatively inexpensive, and are therefore suitable for high-volume printing.
However, since conventional dye inks and pigmented inks have low penetration capability, they are not easily fixed on such commercial printing papers. Therefore, it is difficult to form images on commercial printing papers with conventional dye inks and pigmented inks.
Meanwhile, when printing multivalued image data with, for example, a digital printer or a digital facsimile, dither methods are used to reproduce halftones using halftone levels fewer than original halftone levels. In a dither method, halftones are reproduced by a combination of density modulation (intensity modulation) and area coverage modulation.
In a binary dither method, the density value of a pixel at a coordinate point is compared with a corresponding threshold value in a dither matrix and binarized into 1 (printed or illuminated) or 0 (not printed or not illuminated) based on the result of the comparison. This method enables obtaining binarized data for area coverage modulation by just comparing the density values of pixels in image data with threshold values in a dither matrix and therefore enables high-speed processing.
Also, there are dither methods that use three or more values. For example, when forming an image with an inkjet recording apparatus that can form dots in three sizes, three dither matrices are prepared and pixels are classified into four halftone levels: 0 (no dot), 1 (small-size dot), 2 (medium-size dot), and 3 (large-size dot).
There are many types of dither matrices. For example, Bayer dither matrix, random dither matrix, and blue-noise dither matrix are well-known.
With these dither matrices, during area coverage modulation, dots are not concentrated in a particular area but uniformly distributed. Therefore, these dither matrices are classified as dispersion types.
On the other hand, there are dither matrices that are so designed that dots are concentrated around a certain point. These dither matrices are classified as concentration types.
For example, there is a concentration-type dither matrix in which submatrices are arranged so as to form a screen angle (see, for example, patent documents 1 and 2). Patterns formed by concentrated dots are highly visible when printed and therefore hide unevenness in image density caused by, for example, low paper quality or low printing accuracy. Therefore, concentration-type dither matrices are widely used especially in commercial printing.
Patent document 3 discloses a method of producing a mask or a dither matrix made of threshold values with which pixels in multivalued image data are compared to convert the multivalued image data into a halftone image.
This method includes steps of a) determining a halftone dot pattern for each of predetermined halftone levels and b) creating a mask with the halftone dot patterns obtained in step a). In step a), halftone dot patterns are determined independently for each halftone level.
Patent document 4 discloses a method of preparing a halftone processing mask used in a tone reproduction method in which, when converting a multi-tone image dot by dot into binarized or multivalued image data using a dither matrix, parts of the multi-tone image with a certain density are converted so as to form a line-based pattern having a predetermined direction and other parts are converted so as to obtain high-pass filter characteristics. The halftone processing mask used in the disclosed method is so designed that the line-based pattern includes dots that always synchronize with a recording sequence matrix of dots formed by a combination of multipassing and interlacing of a serial head.
As described above, commercial printing papers are suitable for high-volume printing. However, since commercial printing papers have lower permeability than inkjet printing papers, even a high penetration pigmented ink with better fixation characteristics may not be quickly fixed on a commercial printing paper. Therefore, beading easily occurs on a commercial printing paper. Also, since inks do not spread smoothly on a commercial printing paper, some pixels may be left unfilled.
Patent document 5 discloses a water-based ink including a polyalkylene oxide derivative. The disclosed water-based ink is user for inkjet recording and has excellent drying characteristics and water resistance. However, the disclosed water-based ink has a high surface tension and is therefore not suitable for printing on a commercial printing paper.
Although concentration-type dither matrices have advantages as described above, they have disadvantages too.
For example, when forming an image using an inkjet recording apparatus, concentration of dots or concentration of ink in an area may cause bleeding or undermine fixation of the ink. It is possible to design a concentration-type dither matrix so that dots are not concentrated excessively. However, in highlight parts of an image, since only a small amount of ink is used, it is preferable to concentrate dots. On the other hand, in shadow parts, when dots are concentrated on a paper on which ink does not spread smoothly, some pixels may be left unfilled and the image quality may be reduced. These two conflicting facts are making it difficult to design an appropriate dither matrix.
To reproduce smooth gradation using a dither matrix, the number of gradation levels of the dither matrix must be larger than that of input pixels.
Generally, there are two methods to increase the number of gradation levels. A first method is to increase the size of a submatrix. A second method is to use multiple submatrices as a unit and thereby to increase the total number of dots (see, for example, patent document 1).
In the first method, when the number of gradation levels increases, the screen frequency decreases. Therefore, the first method is not suitable to produce a high-resolution image with a large number of gradation levels.
The second method makes it possible to increase the number of gradation levels without decreasing the screen frequency. However, since the dot areas (the numbers of dots generated) of submatrices are not always the same, if the ratio between submatrices with a large number of dots and submatrices with a small number of dots is unbalanced, the resulting pattern may look like a texture. Therefore, in the second method, the order of selecting submatrices in dot arrangement is important.
When processing a color image including multiple color planes, such as CMYK or RGB, if all of the color planes are processed using the same dither matrix, secondary or higher colors are formed by overlapping halftone patterns of different colors. When an image is formed in this manner on a paper on which ink does not spread smoothly, irregular white spots may be left in the image and, as a results the image quality is reduced. Also, with a certain printing apparatus where a dominant color is determined by the order of overlapping inks, color distortion may also occur.
Patent document 6 discloses a method of preparing a halftone processing mask and an inkjet recording apparatus using the halftone processing mask. The disclosed halftone processing mask is designed to form line-based patterns in such a manner that the recording sequence can be most effectively performed and makes it possible to form a high-quality image even with a low-resolution inkjet recording apparatus.    [Patent document 1] Japanese Patent Application Publication No. 10-75375    [Patent document 2] Japanese Patent Application Publication No. 2003-259118    [Patent document 3] Japanese Patent Application Publication No. 2003-46777    [Patent document 4] Japanese Patent Application Publication No. 2005-1221    [Patent document 5] Japanese Patent Application Publication No. 2001-139849    [Patent document 6] Japanese Patent Application Publication No. 2005-1221